科研之友
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摘要
A planar point-set X in Euclidean plane is called a k-distance set if there are exactly k different distances among the points in X. The function g(k) denotes the maximum number of points in the Euclidean plane that is a k-distance set. In 1996, Erdos and Fishburn conjectured that for k >= 7, every g(k)-point subset of the plane that determines k different distances is similar to a subset of the triangular lattice. We believe that if g(k) is an increasing function of k, then the conjecture is false. We present data supporting our claim and a method of construction that unifies known optimal point configurations for k >= 3.
- 出版日期2013-12-17
